Extended Graetz problem including streamwise conduction and viscous dissipation in microchannel

Extended Graetz problem in microchannel is analyzed by using eigenfunction expansion to solve the energy equation. The hydrodynamically developed flow is assumed to enter the microchannel with uniform temperature or uniform heat flux boundary condition. The effects of velocity and temperature jump boundary condition on the microchannel wall, streamwise conduction and viscous dissipation are all included. From the temperature field obtained, the local Nusselt number distributions are shown as the dimensionless parameters (Peclet number, Knudsen number, Brinkman number) vary. The fully developed Nusselt number for each boundary condition is obtained also in terms of these parameters.